In many applications where sensor reliability is of utmost importance—for instance safety-critical applications—often multiple sensors are used to measure a same physical parameter. Here, the underlying reliability-increasing principle is redundancy. Unfortunately, introducing redundancy at the level of complete sensors significantly increases the overall cost.
In many cases, even a single sensor already exhibits some internal redundancy. This is often the case in difference measurement bridge circuits such as impedance-based sensors such as for example Wheatstone-based sensors. For instance, in a difference measurement bridge circuit, such as for example but not limited thereto in a piezoresistive pressure sensor, it is common to have two impedances which increase with a physical quantity to be measured (Z1 and Z3 in FIG. 1) and two which decrease with the physical quantity to be measured (Z2 and Z4 in FIG. 1). Up to some technology-related mismatch, there are two pairs of matched devices (Z1|Z3 and Z2|Z4) which should behave nearly identical with respect to environmental variables such as pressure and temperature. By checking the similarity of matched sensing elements (e.g., as compared to the expected processing spread), valuable information related to reliability can be obtained.
In most impedance-based sensors, a physical quantity, e.g. change in pressure, temperature etc., causes a change of impedance, which on its turn changes the balance of the bridge. For future reference, a formal definition of the imbalance of two impedances Zi and Zj (with i, j∈{1; 2; 3; 4}) is introduced:
      δ          i      ,      j        =                              Z          i                ⁡                  (          ω          )                    -                        Z          j                ⁡                  (          ω          )                                              Z          i                ⁡                  (          ω          )                    +                        Z          j                ⁡                  (          ω          )                    
These dimensionless quantities will play a role in the electrical bridge transfer, and will also occur in the redundancy test-equations. For the very frequently occurring case of a resistive bridge, Zi=Ri, with Ri the variable resistances of the sensor unit. Then, the imbalance parameters become:
      δ          i      ,      j        =                    R        i            -              R        j                            R        i            +              R        j            
Conversion of a physical quantity to the electrical domain is done by applying an electrical excitation and sensing the resulting electrical response (FIG. 2).
In a first step, the excitation of the bridge is considered (top row of FIG. 2). There are two ways to excite the bridge: either by applying a voltage over the bridge by means of a voltage source (part (a) of FIG. 2), or by driving a current through the bridge by means of a current source (part (b) of FIG. 2). In both cases, the bottom side of the bridge is typically grounded.
Now the sensing of the bridge output is considered (bottom row of FIG. 2). Here, also two possibilities exist. With voltage-mode sensing (part (c) of FIG. 2) the differential open-circuit voltage Vsense is measured at the output of the bridge (with minimal loading of the bridge: Isense≈0). In contrast, with current-mode sensing the short-circuit current Isense is measured, while actively keeping Vsense≈0.
There is little prior-art on exploiting the internal redundancy of a sensor for increasing the reliability of an overall sensor system. EP1111344 describes an in-range fault detection system for a full Wheatstone bridge element having piezoresistive elements. Two implementations are illustrated, in FIG. 3 and FIG. 4, respectively, i.e. an analog approach and a digital approach. In the above document, a test is implemented which checks whether the common-mode voltage of the bridge output nodes is within a window around the common-mode voltage of the bridge input nodes. Because this test fails under certain mismatch conditions, it can be interpreted as a particular redundancy check. However, it is a disadvantage of the solution proposed in this document that it is not a “complete” test, which can detect all mismatch conditions. This is shown by means of an example. As an example only, it is assumed that R3 and R2 as illustrated in FIG. 3 and FIG. 4 are mismatched: R3=αR2 with α≠1 a factor accounting for the mismatch. It is further assumed that R4 and Ri are mismatched in the same way, for instance because the mismatch has a common cause (e.g., irregularity in a membrane which provides a same mismatch to the resistances, a large temperature gradient over the sensor). Then also R4=αR1. It can be shown that under these circumstances the test does not fail for any a, which clearly shows that even large mismatch conditions could remain undetected. This is most easily demonstrated when using voltage excitation of the bridge: the output voltage INM of the voltage divider R3/R4 is independent of the scale factor α, hence it can be easily recognized that all voltages of the bridge are independent of α, and the common-mode test based on these voltages (which obviously must pass for α=1) passes for all values of α. The same conclusion holds when current excitation of the bridge is used. These conclusions can also be drawn if the common-mode equality check used in EP1111344 is translated into an expression based on imbalances:δ14−δ32≈0When the matching is perfect, this test will be exactly equal to zero. However, in real life there will always be some kind of tolerance on the equality, e.g. due to process tolerances. A window is defined within which differences between both imbalances are considered allowable, e.g. differences up to 10%. In EP1111344, the fault detection system has bridge outputs connected to measuring means in the form of a first circuit portion to provide a common mode voltage. A second circuit portion is used to provide a centering voltage equal to the common mode voltage at the time of sensor calibration and a third circuit portion is used to provide a small window voltage which is a fraction of the bridge voltage. The value of the window voltage is subtracted from the value of the centering voltage at a first summing circuit and the results are each compared to the common mode voltage by comparators which are then determined to be within or without a window of valid values by an OR gate.